Hendrik W. Lenstra: Odd perfect numbers
A "perfect number" is a positive integer that is equal to the sum
of its proper divisors; for example: 28 = 1 + 2 + 4 + 7 + 14. The
study of perfect numbers is as ancient as number theory itself,
but embarrassingly little is known about them. It is no wonder
that number theorists turned their attention to less stubborn
subjects, and that perfect numbers fell out of fashion. No
examples of odd perfect numbers are known, and they are believed
not to exist. In the lecture it will be shown that the universe of
odd perfect numbers, void though it presumably may be, offers rich
challenges from an arithmetic, a constructive, and an algorithmic
point of view.